1. Field of the Invention
The present invention relates to signal processing, and more specifically to orthogonal frequency division multiplexing techniques used in signal transmission and reception.
2. Description of the Related Art
Orthogonal frequency division multiplexing (OFDM) is a signal processing technology well known in the field of communications. In general, OFDM operates by dividing a frequency spectrum into smaller subbands (a.k.a. subcarriers) and modulating these subcarriers with data symbols.
FIG. 1 shows a simplified block diagram of one implementation of a prior-art OFDM transmitter 100. Transmitter 100 receives digital input data and converts the data into analog OFDM signals for transmission. Conversion of the data occurs through sequential steps of data symbol mapping 102, inverse fast Fourier transform (IFFT) processing 104, cyclic prefix appending 106, digital-to-analog conversion (DAC) 108, and spectral shaping 110.
Data symbol mapping block 102 receives binary bits of data, which are divided into groups of finite length. One or more data symbols a[n] are created for each group of bits, using any one of a number of modulation techniques commonly known in the art, such as differential quadrature phase-shift-keying (DQPSK) or quadrature amplitude modulation (QAM). The length of each group and thus the number of input data bits per data symbol is determined by the modulation technique employed.
IFFT 104 subsequently applies each set of N data symbols a[n] to a set of N subcarriers, which are numbered from 0 to N−1, where one data symbol a[n] is paired with each subcarrier. The subcarriers employed by OFDM are arranged orthogonally to one another, so that each subcarrier can be distinguished without intersymbol interference. Each set k of N data symbol a[n] and subcarrier pairs is then converted by IFFT 104 from frequency-domain representations into a time-domain OFDM symbol Sk, consisting of N samples Sk[i], where i equals 0 to N−1. The discrete model for each OFDM symbol Sk may be expressed by Equation (1) as follows:
                                                                                                                       S                    k                                    ⁡                                      [                    i                    ]                                                  =                                ⁢                                                      S                    k                                    ⁡                                      (                                          i                      ⁢                                              T                        N                                                              )                                                                                                                          =                                ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                            a                      ⁡                                              [                        n                        ]                                                              ⁢                                          ⅇ                                              j                        ⁢                                                                              2                            ⁢                            π                                                    N                                                ⁢                        n                        ⁢                                                                                                  ⁢                        ⅈ                                                              ⁢                                          w                      ⁡                                              [                        i                        ]                                                                                                                                                                    =                                ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                            a                      ⁡                                              [                        n                        ]                                                              ⁢                                          c                      ⁡                                              [                                                  i                          ,                          n                                                ]                                                                                                                                                    (        1        )            where T/N is the sample period, w[i] is a discrete window function, and
      c    ⁡          [              i        ,        n            ]        =            ⅇ              j        ⁢                              2            ⁢            π                    N                ⁢        n        ⁢                                  ⁢        ⅈ              ⁢          w      ⁡              [        i        ]            denotes the finite length complex exponential sequence of the subcarriers.
The OFDM symbols Sk are then prepared for transmission. First, a cyclic prefix is inserted at the beginning of each OFDM symbol Sk by cyclic prefix appending 106. This prefix enables the receiver to cope with signal echoes that result from multipath reflections. Next, the OFDM symbols and prefixes are converted from digital format to analog format using digital-to-analog converter (DAC) 108. Finally, the analog output from DAC 108 undergoes spectral shaping by spectral shaping block 110 to produce an OFDM signal for transmission.
As an example of the production of a prior-art OFDM signal, assume that IFFT 104 receives 384 data symbols a[n], where n=0, . . . , 383, and employs N=128 subcarriers. Since one data symbol a[n] in each set of N data symbols a[n] is assigned to each subcarrier, the number of OFDM symbols Sk generated is equal to 3 (384 data symbols a[n] divided by 128 subcarriers). The grouping of data symbols a[n] in the frequency domain is shown in Table I. As shown in Table I, in a prior-art OFDM system, data symbols a[0] to a[127] are assigned to OFDM symbol S0, data symbols a[128] to a[255] are assigned to OFDM symbol S1, and data symbols a[256] to a[383] are assigned to OFDM symbol S2.
TABLE IGROUPING OF DATA SYMBOLS a[n] IN THEFREQUENCY DOMAIN OF A PRIOR-ART OFDM SIGNALSubcarrier Index0123. . .127OFDMa[0]a[1]a[2]a[3]. . .a[127]Symbol 0 (S0)OFDMa[128]a[129]a[130]a[131]. . .a[255]Symbol 1 (S1)OFDMa[256]a[257]A[258]a[259]. . .a[383]Symbol 2 (S2)
Table II shows the grouping of samples Sk[i], where k=0, 1, 2 and i=0, . . . , 127, in the time domain after conversion by IFFT 104. In a prior-art OFDM system, the samples Sk[i] of each OFDM symbol Sk remain grouped together, and the OFDM symbols Sk are transmitted in succession. En other words, samples S0[0] to S0[127] of OFDM symbol S0 are transmitted before samples S1[0] to S1[127] of OFDM symbol S1, which are transmitted before samples S2[0] to S2[127] of OFDM symbol S2.
TABLE IIGROUPING OF SAMPLES Sk[i] IN THE TIME DOMAIN OF A PRIOR-ART OFDM SIGNALOFDM Symbol S0OFDM Symbol S1OFDM Symbol S2Sample Index0123. . .127128129130131. . .255256257258259. . .383TransmittedS0[0]S0[1]S0[2]S0[3]. . .S0[127]S1[0]S1[1]S1[2]S1[3]. . .S1[127]S2[0]S2[1]S2[2]S2[3]. . .S2[127]Data
FIG. 2 shows a frequency-domain representation of prior-art OFDM symbol S0 described in the example above. Each subcarrier, represented by a single waveform, is assigned one data symbol a[n]. Additionally, note that the subcarriers are spaced apart so that the peak of each subcarrier corresponds to a zero level of every other subcarrier. This is representative of the orthogonal nature of the set of subcarriers.
FIG. 3 shows a simplified block diagram of one implementation of a prior-art OFDM receiver 300, which reverses the operations performed by OFDM transmitter 100. Receiver 300 receives analog OFDM signals and extracts the original digital data. Extraction occurs through sequential steps of matched filtering 302, analog-to-digital conversion (ADC) 304, cyclic prefix removal 306, fast Fourier transform (FFT) processing 308, and data symbol demapping 310.
First, the received OFDM signal is down-converted into a baseband analog signal at the receiver's RF front end. The baseband analog signal is filtered by matched filtering block 302 and converted to digital format by ADC 304. Next, synchronization and channel estimation may be performed (not shown). Then, cyclic prefix removal block 306 removes the cyclic prefixes from the time-domain OFDM symbols Sk.
FFT 308 receives digital OFDM symbols Sk and extracts the N subcarriers from each to obtain data symbols a[n], according to Equation (2) as follows:
                              a          ⁡                      [            n            ]                          =                              ∑                          i              =              0                                      N              -              1                                ⁢                                                    S                k                            ⁡                              [                i                ]                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                      2                    ⁢                    π                                    N                                ⁢                n                ⁢                                                                  ⁢                i                                      ⁢                          w              ⁡                              [                n                ]                                                                        (        2        )            Finally, data symbols a[n] are demapped into the original binary bits using data symbol demapping block 310 which demodulates the data symbols in accordance with the modulation technique employed by data symbol mapping 102 of FIG. 1.